Statistical arrays

[Castorp]

Challenge: How to create a 10k resistor, using 5x 10k resistors?

Like this?

I'll use the opportunity to give a little update on the excess noise tests. It got a bit uglier than I expected - some parts show considerable batch-to-batch variation, even for batches with recent date codes. But on the positive side, there are new low-noise champions - NOMC (not NOMCA), TDP, HTRN - they stand next to ORN. I'm waiting for a few more samples to test before I wrap this up.

[branadic]

Meh, not fair that you already gave a solution, as you are into it

-branadic-

[Andreas]

Meh, not fair that you already gave the solution, as you are into it

Throwing one of the 5 away would be an equivalent solution.
Through R3 there is no current flow if all other resistors are equal.

With best regards

Andreas

[Castorp]

Finally managed to tick this one off the list. I hope it would be useful.

https://arxiv.org/pdf/2109.02448

[Kleinstein]

The test uses AC voltage (square wave) to test the resistance. For most mechanisms this should be OK, but there may be mechanisms that could react different with DC. That is the resistance fluctuations may be directional. It is still an ingenious method to measure the resistor noise to a very low level. AC modulation of the excitation allows using conventional, no AZ type amplifiers at the critical point.

The more standard (old) way uses DC excitation for the bridge and a chopper or similar amplifier with very low 1/f noise. The noise level for the chopped  amplfiers is usally higher and thus less sensitivty. With modern AZ OPs this still works reasonably well to at least detect the more noise ones.

I see no surprise to sometimes get a higher noise index for the higher value resistors. The very high values could use a thinner film and thus less resistor material. In addition the surface is possibly more prone to noise than the bulk.

There could be a difference between using a thinner film as simple block or a thicker film and than a more fine line pattern. This may also change with value. The substate roughtness may have an indirect effect: a rougher surface makes it more difficult to etch finer patterns.

[branadic]

Wonderful paper, thanks Castrop. 
An explaination why some thinfilm resistors on ceramics show less excess noise compared to others could be, that some manufacturer have their ceramics polished before processing them, though an expensive process. Glass has low surface roughness, but bad thermal conductivity, hence why some manufacturers use silicon instead, which is a good compromise between both and a comparable cheap substrate, given that there is a mass production industry for it.

-branadic-

[Castorp]

Yes, high purity Alumina can be polished well, or it can be glazed. Those are the substrates used by Susumu:
https://global.kyocera.com/prdct/fc/product/pdf/electronic.pdf

It's not so surprising that 96% Alumina yields much noisier resistors. Such substrates are typically used for thick films.

In any case, there must be several factors contributing. It's impossible to separate their effects unless you can fabricate and test many samples of each technology. I strongly suspect that in many cases noise in the contacts dominates, but I really can't prove it conclusively from these measurements.

I have data for some of the parts under pure DC bias. NOMCA and TOMC show the same noise levels as in the square wave test. NOMC, TDP, VHD, SMNZ - they don't show any hidden DC-only noise either, at least to the measurement sensitivity limits. At some point I tried to degrade some low-resistance parts and make them noisy by applying high bias for several days. It didn't work - I guess electromigration needs longer time or higher temperature (or both) to starting showing in the excess noise.

[dietert1]

From the paper i understand that the excess noise index definition includes another factor 1 000 000, since noise is measured in uVrms. Simply speaking a noise index of -40 dB means something like -120 dB + -40 dB = - 160 dB in relation to the DC excitation. Is this correct? I mean ignoring some factors 2 or pi that will enter when looking at bandwidths etc.

When looking up those tiny MPM parts favored by low excess noise results, i was wondering whether a low power => high resistance solution will always perform better. Recently i have been looking at the schematic of the Advantest R6581A and when i see they used dividers made of 17K and 19K to process reference voltages, without any filter caps, pickup from digital parts of the circuit can be much more than -160 dB. Maybe sometimes low noise design may favor lower resistance parts that are a little bigger to stay cool while handling the extra mWs of power.

Regards, Dieter

[Kleinstein]

Yes the noise index definition include those extra -120 dB to start with, but it is also comparing noise from 1 decade to DC. So there is some slightly arbitrary factor already, it could have been 3 decades or a factor or 2 or e as well.
The excess noise is one part of low frequency fluctuations, but there are also possible thermal effects. For those thermal effects low power consumption helps. Otherwise a higher resistance does not reduce the 1/f noise, it more adds the classic Johnson noise and makes the current noise of OPs more visible.  Higher resistor values make the contacts a little less important.  Averaging with a parallel / series circuit is also effective with the excess noise. So using 2 resistors in series or parallel reduces the excess noise by 3 dB.
 
I think that not using filter caps for the reference amplification is a bad idea in the R6581T circuit. Caps won't help with the very low frequency part like < 1Hz , but they work quite well with the faster part of some 10-100 kHz or so, that can be modulated back to the near DC range with the reference modulation in the ADC. So the ADC may react to higher frequency noise of the reference with a kind of aliasing of the reference noise. Chances are they just did not see this less obvious noise path. It is not a large noise contribution (but the LTz1000 noise is still higher than usual OP noise), but easy to avoid.

[dietert1]

So let's say: Resistor excess noise is a consideration for somebody who has reached a precision level of 0.1 ppm and wants to improve. This may apply to several readers here ("voltnuts"). With "bad" resistors like Nomca they will be limited at about 0.03 ppm and with "good" resistors like MPM they will be limited at 0.0003 ppm level - if they ever get there.

I am just trying to put the resistor excess noise discussion and N. Beevs research into perspective. Noise measurements at a -180 or -190 dB level are extremely difficult (near impossible). Don't know if anybody else can do it to confirm the results.

Regards, Dieter

[Kleinstein]

With a relatively normal AZ OP (e.g. LTC2057 for 10 K resistor, AD8628 for 100 K)  on can do the more classical measurement of excess noise with a DC bridge. With some patience (e.g. 10 min taking data) one can see the excess noise down to about a -50 dB noise index  (maybe a little less with more patience and a suitable resistor value).  This is good enough for most applications, except the very demanding ones.
I have done the test with some thin film resistors (Susumu RR 0805 , 4 K - somewhat comparable to the RM networks) to just see a little excess noise, but not really enough to get a number.
The description in the ariticle is very deailed, so it should be able to repat the experiment, at least to the -60dB range. Good amplifiers are better than the Johnson noise - so it is more about patience, thermal stability than a super low noise amplifier.

I see the difference in noise between NOMCA and ORN type resistors with my ADC circuit: with NOMCA resistors the noise is at about 800 nV, with ORN resistors I get something like 500 nV for 1 PLC.   The resistors were the main source of 1/f noise, more than OPA140 or OP7 op-amps.
A rather demanding case for the resistors is something like inverting a 10 V signal with a classic inverter with 2 resistors to set the gain. So 10 V at the resistors. 0.1 to 10 Hz are 2 decades and 2 resistors contributing to the noise with a gain of 1/2. So  with 0 dB noise index one would get 1 ppm of 10 V and thus some 10 µV_RMS for the noise. With a -40 dB noise index this would be 100 nV RMS or some 600 nV_pp. This would still be more than the noise of a standard precision OP like the OP07.

Not many voltage reference are better than 600 nV_pp at 10 V - so often the excess noise is not that important, unless there is bridge of some type (e.g. in a DAC or ADC) were the reference  part is compensated near zero.

The NOMCA resistors are not even that bad - I had similar noise with other thin film resistors.

[branadic]

Refering to my LTFLU experiements I reported large reference noise using NOMCA networks. Own resistor current noise measurements revealed that TOMC has smaller excess noise compared to TOMC, hence why I redesigned the LTFLU board for TOMC networks and its physically larger package. The board with the same LTFLU had much smaller noise then.
With the results now given by Nikolai I could have simply replaced the NOMCA network with a NOMC, which seems to have even lower excess noise compared to TOMC. Maybe I give it a try at some point.

-branadic-

[dietert1]

That's not a confirmation of N. Beevs publication, sorry.

And if an ADC with about 20 V input range improves noise from 800 nV to 500 nV, that's about going from 0.04 ppm to below. I think Kleinstein did see the -30 dB noise index of the Nomcas vanish when choosing better parts, but he did not measure the -70 dB excess noise index of the MPMs. That's another factor 100 less.

Regards, Dieter

[Kleinstein]

Measuring to -70 dB noise index is hard and the way with AC excitation would be the way to go.  The description is quite detailed and if wanted one could repeat it. With well matched resistors to test, the quality of the reference souces should not be that critical   (if needed filter reference noise at around the modulation frequency - so make sure the sources don't have much 400 Hz noise). So I don't think the LTZ1000 sources are really needed.

For resistors not too large or too small (e.g. 5 - 50 K range) the -70 dB range seems doable with patience (it may need a day or two to measure - but hey it probably takes a week of more to build up the setup). Thermal stability and the Johnson noise would be kind of limiting. The excess noise gets larger than the Johnson noise only at really low frequencies. So no matter how good the amplifier, it would need time.

A special build circuit (excitation + AC amplifier and ADC (no need for magic here) and µC for control and demodulation) could be relatively simple. Progamming is still quite a bit of effort for a special build "instrument". The amplifier may be usable for more classic tasks too.
The setup is a bit like a good DMS readout, just also for higher resistance.

[Castorp]

I think Dieter raises some pretty valid points. But there are two aspects here - one is the measurement of very low levels of 1/f noise, the other one is whether this noise would be relevant in any actual application.

The measurement is in fact not that difficult. It should not be seen as a >180 dB dynamic range measurement because it just isn't - it's a measurement of a tiny signal that is amplified. More crucially - the signal can be separated from most of the background noise. That's nothing new - those who do research on thin films have been measuring very low excess noise using lock-in amplifiers and other phase-sensitive methods for many decades. Most of their literature is not relevant for our purposes, because the thin films are exotic types that are far from being part of practical resistors. Also, in these papers they usually don't use the Noise Index but they quantify the results in other ways.

About the practical value of the results - roughly speaking, for certain applications in metrology it could make a big difference whether you have -30 dB or -40 dB. Some colleagues already gave good examples. For some of our applications we need -50 dB to make resistor noise negligible. I doubt it would matter for anyone whether they have -60 dB or lower, because in any practical system there would be other limiting factors (noise of AZ amps, thermal drift, etc.)

In any case, quantitative knowledge is always an advantage. Even if it's just semi-quantitative (like the upper limits). Even if it's just for reassurance.

[Kleinstein]

If there is an application that would be so sensitive to the extra noise  to really need super low noier index, it would also allow to measure the noise. If you can not measure it, it also means it has not effect on the application.

It is still from the physical side interesting to understand the reason behing the 1/f noise. It may correlate with other properties, especially aging. Unstable details that can flicker between 2 states with a slightly higher or lower resistance can also on the long run shift more to 1 side and this way cause drift.

[ramon]

The LT5400 are not of NiCr but SiCr material (Tyler Hutchison, design note 502).

The SiCr material has two times more resistivity (sheet resistance) than NiCr. This could explain why they can have 1M ohm resistors while other networks just go up to 100K only. And why they have higher than average noise of LT5400 compared to other resistors (NiCr over Silicon substrate).

There are also some nice documents google from Vishay and from 'Vishay Elecro-Films' (EFI) that talks about different substrates properties and materials (Al2O3, BeO, AlN, Tamelox ...). With tables and numbers about surface roughness, among many other data.

[Castorp]

Thanks for the info, Ramon! I was aware of this DN but somehow I missed the film type. I'm not sure who told me it's NiCr. I did ask ADI about the substrate and they confirmed it's Si. I'll fix the film type in the next revision of the paper.

I guess you're referring to this table (or something similar):
https://www.vishay.com/company/brands/electro-films/Substrates.html

Too bad there are no readily available resistor networks on any other substrates, just Alumina and silicon. I've heard about custom ones on sapphire or AlN but I've never seen them. Also high purity Alumina substrates vary quite a bit between the suppliers.

[ramon]

Yes, that is the table with the surface information. I think that I saw it in pdf format in a technical document about thin film (with many other tables).

Vishay has NiCr on AlN substrate resistors, but no resistor networks yet.

I guess that the other types of substrates are too expensive or require too much special processing. Not suitable for volume/production. So they just offer them as custom (for microwave high-speed, aerospace,  ...). I haven't seen them too, not even as wire bondable chip.

[dietert1]

How do those historical HP fineline arrays used in their lab grade meters compare in this context? Are they low noise?

Regards, Dieter

[Kleinstein]

At least the resistors (inside U180) in the HP3458 must be reasonable low noise (e.g. noise index better than some -50 dB). There is very little extra noise not explained by known souces (to a large part the simple Johnson noise of the resistors at the integrator input and the OP (LT1001) at the integrator.

The circuit with mixed 40K and 50K resitors and the longer integration time (10 PLC) makes it more sensitive to excess noise than my ADC design.

The fine line construction makes it a good candidate for low noise, as the film can be relatively thick.

[dietert1]

Are you saying those are thick film resistors?

[Kleinstein]

The resistors in HPs fine line technique are still thin film, just a film that can be a little thicker and thus less surface effect. So thick is relative, like 200 nm compared to 100 nm (I  don't know the numbers - just a rough guess)  and than the latteral width smaller due to good lateral resolution in the etching.

Thick film resistors use a different material (usually more like polymer with metal / oxide particles). Due to the production technique with a mask / screen printing they can not at all produce fine lines, but use much coarser lateral structures.

The naming it not really from the film thickneess but the quitestion on how the pattern is defined: thin film starts with a closed film and that uses etching. Think film directly prints the pattern.  So the foil resistors or a PCB are more like thin film technique.   

[iMo]

Is there any way to calculate the "closest divider ratio with max N resistors" (let say with all N resistors equal at the beginning, but finally each one with a resistance value and a TC value) for "ANY possible wirings they can produce"?

Like generating a possible resistor arrangement (especially interesting with none equal resistors), then evaluate the voltage ratio in all created wiring nodes, and picking up the best fits.. And so on with a next new arrangement..

Sounds like as a pretty interesting problem.. Except some theoretical papers talking the total resistance of such sets, I have not found an answer (or application) for the "divider problem" yet (but I am not g..ling for too long, frankly).

[branadic]

I couldn't find anything by now, hence why I wrote this short article:

Resistor ratio dividers based on N equal resistors

-branadic-